Sunday, March 20, 2011

Experience in Infinity

Well, that was a nice vacation. It was great seeing some of my cousins again for the first time in a few years, I played the piano more than I do on a typical day at home, and I also learned a fair bit about stargazing. This evening, though, as promised, I'm going to talk about infinity.

The focus is not mathematical infinity, mind you. There are plenty of interesting things about infinity from a mathematical standpoint, such as the fact that any number divided by infinity would pretty much be zero, and conversely that any number divided by zero is pretty much infinity. There's the fact that you can remove an infinite number of infinite sets from infinity and (if you choose the right sets) still have an infinite set: for instance, if you remove all even numbers from the set of all integers, you can still take out the infinite sets of numbers that are products of numbers greater than 1 and 37, 31, 29, 19, 17, 13, 7, 5, and 3 and still have the infinite set of prime numbers, as well as a sprinkling of other integers. This property may be useful to remember, but again our focus here won't be mathematics. These sets (such as all even integers) are more specifically called transfinite sets.

Instead, let's hop back to the many worlds interpretation of quantum physics we talked about in the previous post. It's worth noting that this interpretation won't give us infinity unless we already have one. That is, unless time and/or space is already infinite, there's always a finite number of alternative worlds created by differences in how the randomness of quantum behavior unfolds. Fortunately for our coming speculation, Big Bang cosmologists tend to agree that space is, indeed, infinite, and those physicists who reject Big Bang theory typically hold instead that time is infinite.

An interesting thing about an infinite universe is that the probability of any event that is at all possible taking place is one. In fact, every possible event occurs an infinite number of times in an infinite universe. It's useful to make an analogue to math here. Suppose we live in a universe (represented by a set of numbers) that is not finite. Every event (represented by a number in that set) that takes place (occurs in the set) is a possible event (it is not excluded by the rules that define the set). We might do better to model our specific corner of the universe with the set of integers rather than the set of all real numbers, because physical change always occurs in quantities that are greater than Planck's constant. So the set of physically possible events (the set of numbers modeling our universe) is restricted to those that differ from each other by at least Planck's constant, similarly to how the set of integers differ from each other by at least one. Nonetheless, we still have an infinite set of possible events. The above is here to show that restricting the events in our set to the possible does not require that the set not be infinite.

While there is surely a lot more we could do with our quantificational faculties about such an infinite universe, let's instead see how our pattern-recognition capabilities would fare. Well, first of all, the whole history of Earth and the solar system exactly as we know it would be enacted endlessly at different places or times in a universe like ours seems to be. There would also be an infinite number of systems that (if you look within specific confines) appeared exactly as ours did up until this moment, when they begin to be ripped away towards a closely passing supermassive black hole. And a great many other permutations could emerge where the resemblance of this alternate Earth system in the infinite set to our own is very nearly perfect, as could ones with less resemblance. So if you are destroyed by the shadow side of humans and the society they have created for themselves, be a bit content in knowing that an infinite of people nearly exactly resembling you are instead flourishing in the benefits of humanity and their social organization. And contraparallel to that, if you know only the contentment of a full stomach, know that a similar infinity of people like you in all respects besides this have already starved to death.

Another peculiar consequence of living in an infinite universe is that there is an limitless number of beings whose experience matches exactly with what you are experiencing right now, even with the complexity required in a brain capable of reading. What's truly strange, though, is that not all of these beings have experiences like this during their waking lives. Some of them are dreaming that they are you. In reflection of that, all of your dreams correspond exactly with the waking experiences of beings on other folds of probability, time, or space.

One of the most provocative ideas that finds itself raised over and over again throughout human history is the idea that, in the same way things vibrating at the same frequency transmit energy to each other, things with the same arrangement transmit information to one another. So far the possibility has escaped both our ability to irrevocably prove or disprove it. Combined with the idea that the universe is infinite this yields frighteningly wondrous consequences.

Have you ever had a thought that felt slightly out of place, or an idea that seemed to come to you from out of nowhere? Perhaps its something that worked its way to you from the mind of another being that was dreaming themselves as you... Of course, if this principle is at work, it is fundamentally interwoven into our experience of mind.